14 research outputs found

    The ideal trefoil knot

    Get PDF
    The most tight conformation of the trefoil knot found by the SONO algorithm is presented. Structure of the set of its self-contact points is analyzed.Comment: 11 pages, 8 figure

    The Physics of the B Factories

    Get PDF

    Limits and applications of group algebras for parameterized problems

    No full text
    The algebraic framework introduced in [Koutis, Proc. of the 35 th ICALP 2008] reduces several combinatorial problems in parameterized complexity to the problem of detecting multilinear degree-k monomials in polynomials presented as circuits. The best known (randomized) algorithm for this problem requires only O ∗ (2 k) time and oracle access to an arithmetic circuit, i.e. the ability to evaluate the circuit on elements from a suitable group algebra. This algorithm has been used to obtain the best known algorithms for several parameterized problems. In this paper we use communication complexity to show that the O ∗ (2 k) algorithm is essentially optimal within this evaluation oracle framework. On the positive side, we give new applications of the method: finding a copy of a given tree on k nodes, a spanning tree with at least k leaves, a minimum set of nodes that dominate at least t nodes, and an m-dimensional k-matching. In each case we achieve a faster algorithm than what was known. We also apply the algebraic method to problems in exact counting. Among other results, we show that a combination of dynamic programming and a variation of the algebraic method can break the trivial upper bounds for exact parameterized counting in fairly general settings.
    corecore